Iterated fractional Brownian motion: Tail estimates and large deviations

We discuss a composition of stochastic processes called iterated fractional Brownian motion. As a consequence of the work of Viens and Vizcarra we are able to determine almost sure moduli of continuity for a large class of iterated fractional Brownian motions. From this we establish a weaker analogue of the uniform modulus of continuity result of Khoshnevisan and Lewis. Next we study the large deviations of iterated fractional Brownian Motion and we relate it to the work of Arcones. We are able to recover his large deviation formulas as a corollary to the main theorem in chapter 4. Finally we make observations that point to similarity's with asymptotic phenomena in statistical physics, most notable the study of the limiting density of iterated random walk by Turban.